Excellent questions! It isn’t a measurement issue because we’ve actually measured the uncertainty. The uncertainty principle can be expressed as a mathematical equation, which you can then go onto use to derive all the rest of quantum. We’ve used those to create and understand new technologies, like the electron tunneling microscope. Electron tunneling is also the underlying phenomenon behind chemical bonding.
As far as why it’s impossible to know the exact position and speed of an object, the answer isn’t very satisfying – it’s just how the universe works. Learning quantum at first requires a suspension of disbelief to some extent, and it’s not one you need to do on faith. If you look up the double slit experiment, it’s a rather simple setup which demonstrates wave-particle duality, and how observing a wavefunction collapses it. It shows us that uncertainty and quantum fuckery is part of the natural world.
One immediate follow-up question is why we can know the exact position and speed of objects in our everyday lives, which again, is a very good question. The uncertainty principle technically states that we can’t know the exact position and momentum of objects. If we let dX represent uncertainty in position, dP uncertainty in momentum, and dV uncertainty in velocity:
dX * dP = constant
Momentum is just mass times velocity, so:
dX * m * dV = constant
dX * dV = constant/m
This tells us that the product of uncertainty is going to be inversely proportional to the mass of an object. So the bigger something is, the less uncertainty there is about its position and velocity. When something gets really small, say atomic and subatomic sizes, the uncertainty gets very large.
Sorry if this is way more detail than you wanted. I took a few classes in college that touched on quantum, and Physical Chemistry was pretty much all just quantum. I had an excellent professor for it that showed us how you could derive all of it from the uncertainty principle.